Problem Statement

You are given a sequence A=(A_1,A_2,\dots,A_N) of length N and a sequence B=(B_1,B_2,\dots,B_M) of length M. Here, all elements of A and B are pairwise distinct. Determine whether the sequence C=(C_1,C_2,\dots,C_{N+M}) formed by sorting all elements of A and B in ascending order contains two consecutive elements appearing in A.

Constraints

• 1 \leq N, M \leq 100
• 1 \leq A_i, B_j \leq 200
• A_1, A_2, \dots, A_N, B_1, B_2, \dots, B_M are distinct.
• All input values are integers.

Sample Input 1

3 2
3 2 5
4 1

Sample Output 1

Yes

C=(1,2,3,4,5). Since 2 and 3 from A occur consecutively in C, print Yes.

Sample Input 2

3 2
3 1 5
4 2

Sample Output 2

No

C=(1,2,3,4,5). Since no two elements from A occur consecutively in C, print No.

Sample Input 3

1 1
1
2

Sample Output 3

No

Problem Statement

From the point (0,0) in a two-dimensional plane, let us move the distance of 1 toward the point (A, B). Find our coordinates after the move.

Here, after moving the distance of d from a point X to a point Y (d \le length of the segment XY), we are at the point on the segment XY whose distance from X is d.
The Constraints guarantee that the distance between the points (0, 0) and (A, B) is at least 1.

Constraints

• All values in input are integers.
• 0 \le A,B \le 1000
• (A,B) \neq (0,0)

Sample Input 1

3 4

Sample Output 1

0.600000000000 0.800000000000

Printing 0.5999999999 0.8000000001, for example, would also be accepted.

Sample Input 2

1 0

Sample Output 2

1.000000000000 0.000000000000

We may arrive at (A, B).

Sample Input 3

246 402

Sample Output 3

0.521964870245 0.852966983083

Problem Statement

There are N creatures standing in a circle, called Snuke 1, 2, ..., N in counter-clockwise order.

When Snuke i (1 \leq i \leq N) receives a gem at time t, S_i units of time later, it will hand that gem to Snuke i+1 at time t+S_i. Here, Snuke N+1 is Snuke 1.

Additionally, Takahashi will hand a gem to Snuke i at time T_i.

For each i (1 \leq i \leq N), find the time when Snuke i receives a gem for the first time. Assume that it takes a negligible time to hand a gem.

Constraints

• 1 \leq N \leq 200000
• 1 \leq S_i,T_i \leq 10^9
• All values in input are integers.

Sample Input 1

3
4 1 5
3 10 100

Sample Output 1

3
7
8

We will list the three Snuke's and Takahashi's actions up to time 13 in chronological order.

Time 3: Takahashi hands a gem to Snuke 1.

Time 7: Snuke 1 hands a gem to Snuke 2.

Time 8: Snuke 2 hands a gem to Snuke 3.

Time 10: Takahashi hands a gem to Snuke 2.

Time 11: Snuke 2 hands a gem to Snuke 3.

Time 13: Snuke 3 hands a gem to Snuke 1.

After that, they will continue handing gems, though it will be irrelevant to the answer.

Sample Input 2

4
100 100 100 100
1 1 1 1

Sample Output 2

1
1
1
1

Note that the values S_i and T_i may not be distinct.

Sample Input 3

4
1 2 3 4
1 2 4 7

Sample Output 3

1
2
4
7

Note that a Snuke may perform multiple transactions simultaneously. Particularly, a Snuke may receive gems simultaneously from Takahashi and another Snuke.

Sample Input 4

8
84 87 78 16 94 36 87 93
50 22 63 28 91 60 64 27

Sample Output 4

50
22
63
28
44
60
64
27

Problem Statement

Takahashi has two sheets A and B, each composed of black squares and transparent squares, and an infinitely large sheet C composed of transparent squares.
There is also an ideal sheet X for Takahashi composed of black squares and transparent squares.

The sizes of sheets A, B, and X are H_A rows \times W_A columns, H_B rows \times W_B columns, and H_X rows \times W_X columns, respectively.
The squares of sheet A are represented by H_A strings of length W_A, A_1, A_2, \ldots, A_{H_A} consisting of . and #.
If the j-th character (1\leq j\leq W_A) of A_i (1\leq i\leq H_A) is ., the square at the i-th row from the top and j-th column from the left is transparent; if it is #, that square is black.
Similarly, the squares of sheets B and X are represented by H_B strings of length W_B, B_1, B_2, \ldots, B_{H_B}, and H_X strings of length W_X, X_1, X_2, \ldots, X_{H_X}, respectively.

Takahashi's goal is to create sheet X using all black squares in sheets A and B by following the steps below with sheets A, B, and C.

1. Paste sheets A and B onto sheet C along the grid. Each sheet can be pasted anywhere by translating it, but it cannot be cut or rotated.
2. Cut out an H_X\times W_X area from sheet C along the grid. Here, a square of the cut-out sheet will be black if a black square of sheet A or B is pasted there, and transparent otherwise.

Determine whether Takahashi can achieve his goal by appropriately choosing the positions where the sheets are pasted and the area to cut out, that is, whether he can satisfy both of the following conditions.

• The cut-out sheet includes all black squares of sheets A and B. The black squares of sheets A and B may overlap on the cut-out sheet.
• The cut-out sheet coincides sheet X without rotating or flipping.

Constraints

• 1\leq H_A, W_A, H_B, W_B, H_X, W_X\leq 10
• H_A, W_A, H_B, W_B, H_X, W_X are integers.
• A_i is a string of length W_A consisting of . and #.
• B_i is a string of length W_B consisting of . and #.
• X_i is a string of length W_X consisting of . and #.
• Sheets A, B, and X each contain at least one black square.

Sample Input 1

3 5
#.#..
.....
.#...
2 2
#.
.#
5 3
...
#.#
.#.
.#.
...

Sample Output 1

Yes

First, paste sheet A onto sheet C, as shown in the figure below.

     \vdots
  .......  
  .#.#...  
\cdots.......\cdots
  ..#....  
  .......  
     \vdots

Next, paste sheet B so that its top-left corner aligns with that of sheet A, as shown in the figure below.

     \vdots
  .......  
  .#.#...  
\cdots..#....\cdots
  ..#....  
  .......  
     \vdots

Now, cut out a 5\times 3 area with the square in the first row and second column of the range illustrated above as the top-left corner, as shown in the figure below.

...
#.#
.#.
.#.
...

This includes all black squares of sheets A and B and matches sheet X, satisfying the conditions.

Therefore, print Yes.

Sample Input 2

2 2
#.
.#
2 2
#.
.#
2 2
##
##

Sample Output 2

No

Note that sheets A and B may not be rotated or flipped when pasting them.

Sample Input 3

1 1
#
1 2
##
1 1
#

Sample Output 3

No

No matter how you paste or cut, you cannot cut out a sheet that includes all black squares of sheet B, so you cannot satisfy the first condition. Therefore, print No.

Sample Input 4

3 3
###
...
...
3 3
#..
#..
#..
3 3
..#
..#
###

Sample Output 4

Yes

Problem Statement

Takahashi will receive N presents.

He has a parameter called mood, which is a non-negative integer, and his mood changes every time he receives a present. Each present has three parameters: value P, mood increase A, and mood decrease B, and his mood changes as follows based on these parameters:

• When the value P of the received present is greater than or equal to his mood, he is happy with the present, and his mood increases by A.
• When the value P of the received present is less than his mood, he is disappointed with the present, and his mood decreases by B. However, if his mood is originally less than B, it becomes 0.

The i-th (1\le i\le N) present he receives has value P _ i, mood increase A _ i, and mood decrease B _ i.

You are given Q questions, so answer all of them. In the i-th (1\le i\le Q) question, you are given a non-negative integer X _ i, so answer the following question:

Find Takahashi's mood after receiving all N presents when his mood is initially X _ i.

Constraints

• 1\le N\le10000
• 1\le P _ i\le500\ (1\le i\le N)
• 1\le A _ i\le500\ (1\le i\le N)
• 1\le B _ i\le500\ (1\le i\le N)
• 1\le Q\le5\times10 ^ 5
• 0\le X _ i\le10 ^ 9\ (1\le i\le Q)
• All input values are integers.

Sample Input 1

4
3 1 4
1 5 9
2 6 5
3 5 8
11
0
1
2
3
4
5
6
7
8
9
10

Sample Output 1

6
0
0
0
5
6
0
0
0
0
0

When Takahashi's initial mood is 10, his mood changes as follows:

• The value 3 of the first present is less than his mood 10, so his mood decreases by the mood decrease 4, and his mood becomes 6.
• The value 1 of the second present is less than his mood 6, and Takahashi's mood 6 is less than the mood decrease 9, so his mood becomes 0.
• The value 2 of the third present is not less than his mood 0, so his mood increases by the mood increase 6, and his mood becomes 6.
• The value 3 of the fourth present is less than his mood 6, and Takahashi's mood 6 is less than the mood decrease 8, so his mood becomes 0.

Therefore, his final mood is 0.

Sample Input 2

3
500 500 500
500 500 500
500 500 500
1
1000000000

Sample Output 2

999998500

Because Takahashi's mood is too high, his mood keeps decreasing even when he receives the best presents.

Sample Input 3

20
124 370 105
280 200 420
425 204 302
435 141 334
212 287 231
262 410 481
227 388 466
222 314 366
307 205 401
226 460 452
336 291 119
302 104 432
478 348 292
246 337 403
102 404 371
368 399 417
291 416 351
236 263 231
170 415 482
101 339 184
20
1162
1394
1695
2501
3008
3298
4053
4093
4330
5199
5302
5869
5875
6332
6567
7483
7562
7725
9723
9845

Sample Output 3

339
339
339
339
339
339
339
339
339
339
339
339
339
389
339
643
722
885
2883
3005